arXiv subjects

Mengfan Lyu

Publications and source records attributed to Mengfan Lyu.

5 recordsLinked to original sources

arXiv2025

Permutation closure for multiple context-free languages

We prove that the \emph{permutation closure} of a multiple context-free language is multiple context-free, which extends work of Okhotin and Sorokin [LATA 2020] who showed closure under \emph{cyclic shift}, and complements work of Brandstädt [1981, RAIRO Inform. Théor.] (resp. Brough \emph{et al.} [2016, Discrete Math. Theor. Comput. Sci.]) who showed the same result for regular, context-sensitive, recursively enumerable (resp. EDT0L and ET0L) languages. In contrast to Okhotin and Sorokin who work with grammars, our proof uses restricted tree stack automata due to Denkinger [DLT 2016].

cs.FL↗

arXiv2025

A substitution lemma for multiple context-free languages

We present a necessary condition for an infinite language to be multiple context-free, which we call a Substitution Lemma. We apply it to show a sample selection of languages are not multiple context-free, including the word problem of the group $F_2\times F_2$. We also show that groups with multiple context-free word problem have decidable rational subset membership problem. Our result contrasts with previous work showing that the standard pumping lemma for context-free languages cannot be generalised to multiple context-free languages, and that weak variants of generalised Ogden's lemma do not apply to multiple context-free languages.

cs.FL↗

arXiv2024

Generalised Temperley-Lieb algebras of type $G(r,p,n)$

In an earlier work, we defined a ``generalised Temperley-Lieb algebra'' $TL_{r,1,n}$ corresponding to the imprimitive reflection group $G(r,1,n)$ as a quotient of the cyclotomic Hecke algebra. In this work we introduce the generalised Temperley-Lieb algebra $TL_{r,p,n}$ which corresponds to the complex reflection group $G(r,p,n)$. Our definition identifies $TL_{r,p,n}$ as the fixed-point subalgebra of $TL_{r,1,n}$ under a certain automorphism $σ$. We prove the cellularity of $TL_{r,p,n}$ by proving that $σ$ induces a special shift automorphism with respect to the cellular structure of $TL_{r,1,n}$. We also give a description of the cell modules of $TL_{r,p,n}$ and their decomposition numbers, and finally we point to how our algebras might be categorified and could lead to a diagrammatic theory.

math.RT↗

arXiv2023

Secure and Private Vickrey Auction Protocols: A Secure Multiparty Computation Approach

Recent attention on secure multiparty computation and blockchain technology has garnered new interest in developing auction protocols in a decentralized setting. In this paper, we propose a secure and private Vickrey auction protocol that addresses the challenge of maintaining auction correctness while preserving the confidentiality of bidders' information. Our protocol leverages secure multiparty computation (SMPC) techniques that enable decentralized computation of the final payment price without disclosing additional information. The total computational complexity of our proposed protocol, including preparation, is $O(n^2 k)$, and the complexity for the main auction is $O(n k)$. Furthermore, we show that our protocol is resistant to collusion and the auction outcome is publicly verifiable, which prevents dishonest bidders from altering this outcome.

cs.CR↗

arXiv2022

Generalised Temperley-Lieb algebras of type $G(r,1,n)$

In this paper, we define a quotient of the cyclotomic Hecke algebra of type $G(r,1,n)$ as a generalisation of the Temperley-Lieb algebras of type $A$ and $B$. We establish a graded cellular structure for the generalised Temperley-Lieb algebra and, using the technology of $KLR$ algebras, determine the corresponding decomposition matrix.

math.RT↗